If you want to make a freezer thermos, like the freezer mugs you put in the freezer, you could get a metal container for the inside, and then seal off a section of liquid which has a lot of heat capacity such as those freezer jel packs for icing injuries. The outer layer should be very insulating. Maybe some silver bubble wrap and then fiberglass insulation. If you have a way of doing it, you could make your own aerogel to insulate it. To charge it, shove the whole thing in the freezer, and then take it out, put your ice cream in and then put a lid on it. It will stay frozen, or become a solid block by the time it gets to the picnic. I think I want to make one now, and then do an instructable on it.

If you keep the ice cream (container) on ice, it will stay cold longer.

To add science to the mix: Add salt to the ICE (not the ice cream). The salt will lower the temperature required to keep the ice frozen. To maintain its current energy level, it has to get colder (to maintain the frozen state). Rock salt, sea salt, table salt - any will do.

A thermos is a great way to keep things hot and cold. I made a simple thermos in high school for a science project with teh exact same objective: "keep it cold", my thermos was easy to assemble and it was simple in design. Just grab a clear container, wrap it in foil with the shiny side facing out (to reflect heat on the shiny side and absorb heat on the matte side), then make a housing for the entire container. Done!

Frollards method will work much better than mine, but you may have restrictions as to what you are allowed to use to keep it cold. good luck!

..umm I wrote 'allowed' thinking I was still talking about high school physics again. oops. Make that "but you may have restrictions as to what you are able to use to keep it cold" (the idea being that a bed of ice cubes might make it tough to be portable, I guess it depends on what you intend to do with the ice cream) good luck!